Every radiating solution of the Helmholtz equation has the following asymptotic
behavior at infinity [1]}
\(u^{sc}(x)=\frac{e^{i\frac{\pi }{4}}}{\sqrt{8k\pi }}\frac{e^{ikr}}{\sqrt{r}}\left\lbrace u^{\infty }(\theta _{\hat{x}})+\mathcal {O}\left(\frac{1}{r}\right)\right\rbrace \quad \mbox{as }\,r:=|x|\rightarrow \infty ,\) 
